Integral(x³×ln(√x))dx ?

1 Answer
May 15, 2018

#x^4/8 ln(x) - 1/32 x^4+C#

Explanation:

The integral is

#1/2int x^3 ln (x)dx#

Integrating this by parts, we get

#1/2int x^3 ln (x)dx = 1/2 ln(x) int x^3dx#
#qquad -1/2int[(int x^3dx)times d/dx(ln(x))]dx#
#qquad = x^4/8 ln (x) - 1/8 int [x^4 times 1/x] dx#
#qquad = x^4/8 ln (x) - 1/8 int x^3dx#
#qquad = x^4/8 ln(x) - 1/32 x^4+C#